Asymptotic Optimal Tracking: Feedback Strategies

TL;DR

This paper analyzes feedback strategies for tracking problems, demonstrating their asymptotic optimality in various scenarios despite non-Markovian dynamics, by focusing on current state-dependent control within time-varying domains.

Contribution

It introduces and studies a class of simple, state-dependent feedback strategies that are proven to be asymptotically optimal for a broad range of tracking problems.

Findings

Feedback strategies depend only on current state

Strategies keep deviation within a time-varying domain

Strategies are asymptotically optimal for many examples

Abstract

This is a companion paper to (Cai, Rosenbaum and Tankov, Asymptotic lower bounds for optimal tracking: a linear programming approach, arXiv:1510.04295). We consider a class of strategies of feedback form for the problem of tracking and study their performance under the asymptotic framework of the above reference. The strategies depend only on the current state of the system and keep the deviation from the target inside a time-varying domain. Although the dynamics of the target is non-Markovian, it turns out that such strategies are asympototically optimal for a large list of examples.